Development of a non-overlapping domain decomposition method for problems with boundary layer by Hongru LI

In this talk an effective and novel near-wall domain decomposition approach with non-local interface boundary conditions is developed and tested in application to model equations that simulate high-Reynolds-number flow with a boundary layer. The approach is also compared with existing non-local near-wall domain decomposition approaches in the literature and is proven to be more efficient. The supreme onvergence of the approach is analysed theoretically in Poisson equation and the result is further confirmed to be valid in application to the model equations. Both theoretical and numerical analysis shows that the approach has great potential to be applied to near-wall turbulence modelling.

The non-local interface boundary condition of the approach is obtained by approximating the non-local Steklov-Poincaré operators, which are decomposed into a few basic units under local Taylor expansions. The approximation is proved to be effective in retaining the non-local nature of the operators and is easy to implement. The convergence analysis is performed in two steps: first ignore the boundary effect when analysing the product of Steklov-Poincaré operators applied to given functions (standard analysis); next restore the ignored boundary effect. These two steps reflect the influence of the governing equation and boundary conditions respectively. Together they describe the complete non-local nature of Steklov-Poincaré operators in application to a given problem.